Date of Award

5-2010

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. Joseph W. McKean

Second Advisor

Dr. Jung Chao Wang

Third Advisor

Dr. Bradley E. Huitema

Abstract

This study discusses robust procedures for the analysis of covariance (ANCOVA) models. These methods are based on rank-based (R) fitting procedures, which are quite analogous to the traditional ANCOVA methods based on least squares fits. Our initial empirical results show that the validity of R procedures is similar to the least squares procedures. In terms of power, there is a small loss in efficiency to least squares methods when the random errors have a normal distribution but the rank-based procedures are much more powerful for the heavy-tailed error distributions in our study.

Rank-based analogs are also developed for pick-a-point, adjusted mean, and the Johnson-Neyman procedures. Instead of regions of significance, pick-a-point procedures obtain the confidence interval for treatment differences at any selected covariate point. For the traditional adjusted means procedures, it is established that they can be derived from the underlying design by using the normal equations. This is then used to derive the rank-based adjusted means, showing that they have the desired asymptotic representation. This study compares these with their LS counterparts, the naive adjusted Hodges-Lehmann, and adjusted medians. A rank-based analog is developed for the Johnson-Neyman technique which obtains a region of significant differences of the treatments. Examples illustrate the rank-based procedures. For each of these ANCOVA procedures, Monte Carlo analysis is conducted to compare empirically the differences of the traditional and robust methods. The results indicate that these robust, rank-based, procedures have more power than the traditional least squares for longer-tailed distributions for the situations investigated.

Access Setting

Dissertation-Open Access

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